Question 741917: Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
121y^2-100x^2=12100
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
121y^2-100x^2=12100
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Given hyperbola has a vertical transverse axis. (y-term written before x-term)
Its standard form of equation:  , (h,k)=(x,y) coordinates of center
121y^2-100x^2=12100
divide by 12100
center: (0,0)
transverse axis: vertical
..
a^2=100
a=√100=10
vertices: (0,0±a)=(0,0±10)=(0,-10) and (0,10)
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b^2=121
b=√121=11
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c^2=a^2+b^2=100+121=221
c=√221≈14.87
foci: (0,0±c)=(0,0±14.87)=(0,-14.87) and (0,14.87)
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asymptotes: straight line equations that go thru the center of the form: y=mx+b, m=slope, b=y-intercept.
slopes of asymptotes of hyperbolas with vertical transverse axis=±a/b=±10/11
..
Equation of asymptote with positive slope.
y=10x/11
Equation of asymptote with negative slope.
y=-10x/11
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